2x2 determinants and inverse matrices

2x2 determinants and inverse matrices Quiz

Spec C5–C6 · AQA A-Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Find det⁡(4−325)\det\begin{pmatrix}4&-3\\2&5\end{pmatrix}.

    • A. 1414
    • B. −26-26
    • C. 2626
    • D. 2020

  2. 2. For which value of kk is (k432)\begin{pmatrix}k&4\\3&2\end{pmatrix} singular?

    • A. k=6k=6
    • B. k=2k=2
    • C. k=12k=12
    • D. k=3k=3

  3. 3. Find the inverse of (1235)\begin{pmatrix}1&2\\3&5\end{pmatrix}.

    • A. (5−2−31)\begin{pmatrix}5&-2\\-3&1\end{pmatrix}
    • B. (−5−2−3−1)\begin{pmatrix}-5&-2\\-3&-1\end{pmatrix}
    • C. (−123−5)\begin{pmatrix}-1&2\\3&-5\end{pmatrix}
    • D. (−523−1)\begin{pmatrix}-5&2\\3&-1\end{pmatrix}

  4. 4. A\mathbf{A} and B\mathbf{B} are non-singular 2×22\times2 matrices. What is (AB)−1(\mathbf{A}\mathbf{B})^{-1}?

    • A. A−1B−1\mathbf{A}^{-1}\mathbf{B}^{-1}
    • B. B−1A−1\mathbf{B}^{-1}\mathbf{A}^{-1}
    • C. A−1+B−1\mathbf{A}^{-1}+\mathbf{B}^{-1}
    • D. AB−1\mathbf{A}\mathbf{B}^{-1}

  5. 5. A\mathbf{A} is non-singular and AX=B\mathbf{A}\mathbf{X}=\mathbf{B}. What is X\mathbf{X}?

    • A. BA−1\mathbf{B}\mathbf{A}^{-1}
    • B. BA\mathbf{B}\mathbf{A}
    • C. A−1B\mathbf{A}^{-1}\mathbf{B}
    • D. AB−1\mathbf{A}\mathbf{B}^{-1}

Quiz